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Stochastic Order and MLE of the Mean of the Exponential Distribution

Author

Listed:
  • N. Balakrishnan

    (McMaster University)

  • C. Brain

    (Florida International University)

  • Jie Mi

    (Florida International University)

Abstract

The maximum likelihood estimator of the mean of the exponential distribution, based on various data structures has been studied extensively. However, the order preserving property of these estimators is not found in the literature. This article discusses this property. Suppose that two samples of the same size are drawn from two independent exponential populations that have different means. It is shown in this article that the regular stochastic ordering holds between the two MLEs corresponding to the two exponential means, based on various censored data. In particular, conditions are given on inspection times so that the result is also true for grouped data.

Suggested Citation

  • N. Balakrishnan & C. Brain & Jie Mi, 2002. "Stochastic Order and MLE of the Mean of the Exponential Distribution," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 83-93, March.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:1:d:10.1023_a:1015709631421
    DOI: 10.1023/A:1015709631421
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    References listed on IDEAS

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    1. Gan, Gaoxiong, 1998. "MLE are stochastically increasing if likelihoods are unimodal," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 289-292, October.
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    Cited by:

    1. Nowak, Piotr Bolesław, 2016. "The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 49-54.
    2. N. Balakrishnan & G. Iliopoulos, 2009. "Stochastic monotonicity of the MLE of exponential mean under different censoring schemes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 753-772, September.

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    1. Nowak, Piotr Bolesław, 2016. "The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 49-54.

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